Bet once you get the concrete warm, it will stay warm for a while. I think the specific heat for concrete is about 0.5. Water is 1.0. What this means it is it takes the same energy to heat 2 pounds of concrete as it takes to heat 1 pound of water.
Your slow response is because you have tons of concrete, thermal mass, to warm up.
If it require 24 hours to recover, water heater not shutting off, it would cost me about $15.
Could see the advantage of having dry floors.
I was working in my 24x24 garage today, not shop, which is attached to my house. I can heat it with a 1500 watt baseboard heater. However, I haven't had the heater on in years. The garage temp was 45. Last night it was about 20. My garage has over R20 walls, R50 ceiling, Anderson windows, insulated doors. Leave windows cracked open a little to keep it dryed out. I think the reason my garage stays warm is because it is south facing, brick on the outside, some heat comes through the insulated wall from house and the main reason is my 6 inch concrete floor is resting on 8 inches of pea gravel. The gravel acts as an insulator.
Hope your heating works well for you. Like you said, you could heat the water with anything. May find out propane is cheaper.